The road to publication is filled with conversations. I used to think authors just wrote their stuff, mailed it out, and got published. Everything I've ever published was in some way connected to a conversation I first had with a fellow author, editor, agent, or librarian.
Most of these conversations took place at writing conferences. For folks looking to get on the road to publication, I feel there is no better place to start. When attending it is probably just as important to talk to the people sitting near you in the audience (my first one I unknowingly sat next to Laurie Halse Anderson just before Speak came out) as to those editors and agents after their presentations (talk to them too!)
I met one of my editors in a line at lunch and another milling around in a lobby. Be ready to talk about your work, why it excites you and should excite them. Even if you're not published do not hesitate to identify yourself as a writer (as long as you're writing, right?) wherever you are. I met a parent at a school I worked at, out who turned out to be James Michener's agent. He doesn't handle children's books, but he's proved to be an invaluable sounding board for me over the years.
Since most of my books are actually about math, I will summarize with an equation: Conferences + Conversations = Connections (which equals publications) See. Math can be fun.